Problem: You are given N items.
The value of the i-th item (1 \leq i \leq N) is v_i.
Your have to select at least A and at most B of these items.
Under this condition, find the maximum possible arithmetic mean of the values of selected items.
Additionally, find the number of ways to select items so that the mean of the values of selected items is maximized.

Constraints

* 1 \leq N \leq 50
* 1 \leq A,B \leq N
* 1 \leq v_i \leq 10^{15}
* Each v_i is an integer.

Input

The input is given from Standard Input in the following format:


N A B
v_1
v_2
...
v_N


Output

Print two lines.
The first line should contain the maximum possible arithmetic mean of the values of selected items. The output should be considered correct if the absolute or relative error is at most 10^{-6}.
The second line should contain the number of ways to select items so that the mean of the values of selected items is maximized.

Examples

Input

5 2 2
1 2 3 4 5


Output

4.500000
1


Input

4 2 3
10 20 10 10


Output

15.000000
3


Input

5 1 5
1000000000000000 999999999999999 999999999999998 999999999999997 999999999999996


Output

1000000000000000.000000
1

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;
import java.util.Map.Entry;
import java.util.stream.IntStream;

public class Main {
    static ContestScanner in;
    static Writer out;
    public static void main(String[] args) {
        Main main = new Main();
        try {
            in = new ContestScanner();
            out = new Writer();
            main.solve();
            out.close();
            in.close();
        } catch (IOException e) {
            e.printStackTrace();
        }
    }

    void solve() throws IOException {
        int n = in.nextInt();
        int a = in.nextInt();
        int b = in.nextInt();
        long[] v = new long[n];
        for (int i = 0; i < n; i++) {
            v[i] = in.nextLong();
        }
        Arrays.sort(v);
        long sum = 0;
        for (int i = 0; i < a; i++) {
            sum += v[n - 1 - i];
        }
        long least = v[n - a];
        int lower = 0;
        for(int i = n - a; i < n; i++) {
            if(v[i] != least) break;
            lower++;
        }
        int count = 0;
        for(int i = 0; i < n; i++) {
            if(v[i] == least) count++;
        }
        long[][] comb = pascalT(51);
        int add = b - a;
        long ans = 0;
        if(v[n - 1] == least) {
            for (int i = lower; i <= Math.min(count, lower + add); i++) {
                ans += comb[count][i];
            }
        } else {
            ans = comb[count][lower];
        }
        System.out.println((double)sum / a);
        System.out.println(ans);
    }

    public static long[][] pascalT(int n){
        long[][] tri = new long[n][];
        for(int i=0; i<n; i++){
            tri[i] = new long[i+1];
            for(int j=0; j<i+1; j++){
                if(j == 0 || j == i){
                    tri[i][j] = 1;
                }else{
                    tri[i][j] = tri[i-1][j-1] + tri[i-1][j];
                }
            }
        }
        return tri;
    }
}


class Writer extends PrintWriter{
    public Writer(String filename)throws IOException
    {super(new BufferedWriter(new FileWriter(filename)));}
    public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
    private BufferedReader in;private int c=-2;
    public ContestScanner()throws IOException
    {in=new BufferedReader(new InputStreamReader(System.in));}
    public ContestScanner(String filename)throws IOException
    {in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
    public String nextToken()throws IOException {
        StringBuilder sb=new StringBuilder();
        while((c=in.read())!=-1&&Character.isWhitespace(c));
        while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public String readLine()throws IOException{
        StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
        while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
        return sb.toString();
    }
    public long nextLong()throws IOException,NumberFormatException
    {return Long.parseLong(nextToken());}
    public int nextInt()throws NumberFormatException,IOException
    {return(int)nextLong();}
    public double nextDouble()throws NumberFormatException,IOException
    {return Double.parseDouble(nextToken());}
    public void close() throws IOException {in.close();}
}